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An application-based characterization of dynamical distance geometry problems

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Abstract

The dynamical distance geometry problem (dynDGP) is the problem of finding a realization in a Euclidean space of a weighted undirected graph G representing an animation by relative distances, so that the distances between realized vertices are as close as possible to the edge weights. In the dynDGP, the vertex set of the graph G is the set product of V, representing certain objects, and T, representing time as a sequence of discrete steps. We suppose moreover that distance information is given together with the priority of every distance value. The dynDGP is a special class of the DGP where the dynamics of the problem comes to play an important role. In this work, we propose an application-based characterization of dynDGP instances, where the main criteria are the presence or absence of a skeletal structure, and the rigidity of such a skeletal structure. Examples of considered applications include: multi-robot coordination, crowd simulations, and human motion retargeting.

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Acknowledgements

We wish to thank Douglas S. Gonçalves for the fruitful discussions. This work was partially supported by an INS2I-CNRS 2016 “PEPS” Project, and by the ANR Project ANR-14-CE27-0007 SenseFly.

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Correspondence to Antonio Mucherino.

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Mucherino, A., Omer, J., Hoyet, L. et al. An application-based characterization of dynamical distance geometry problems. Optim Lett 14, 493–507 (2020). https://doi.org/10.1007/s11590-018-1302-6

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Keywords

  • Distance geometry
  • Dynamical problems
  • Motion retargeting
  • Crowd simulations
  • Multi-agent formation